The gravitational polarization tensor of thermal $\lambda\phi^4$ theory

TL;DR

This paper computes the low-momentum gravitational polarization tensor in a thermal scalar field theory using a two-loop resummed perturbation approach that includes thermal mass and nonlocal vertex effects.

Contribution

It introduces an improved perturbation theory for scalar thermal field theory that accounts for thermal mass resummation and nonlocal vertices in gravitational polarization calculations.

Findings

Calculated the gravitational polarization tensor at two-loop order.

Demonstrated the necessity of resumming thermal mass and nonlocal vertices.

Provided insights into the structure of scalar plasma's gravitational response.

Abstract

The low-momentum structure of the gravitational polarization tensor of an ultrarelativistic plasma of scalar particles with $\lambda\phi^4$ interactions is evaluated in a two-loop calculation up to and including order $\lambda^{3/2}$. This turns out to require an improved perturbation theory which resums a local thermal mass term as well as nonlocal hard-thermal-loop vertices of scalar and gravitational fields.